A172018 - OEIS

%I #11 Mar 16 2022 02:54:06

%S 1,4,182,27410,8890310,5051270688,4459786293372,5659222645997646,

%T 9770821427711370950,22041005972637205198568,

%U 62967534725721252354766676,222256499446324679350316816644,950020052553444052606973276792092,4836606673194788521307702032786510240,28920975283745982162014025622769293094712

%N a(n) = A142458(2*n-1, n)/n.

%H G. C. Greubel, <a href="/A172018/b172018.txt">Table of n, a(n) for n = 1..190</a>

%F a(n) = A142458(2*n-1, n)/n.

%t T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];

%t A172018[n_]:= T[2*n-1, n, 3]/n;

%t Table[A172018[n], {n, 30}] (* modified by _G. C. Greubel_, Mar 16 2022 *)

%o (Sage)

%o @CachedFunction

%o def T(n,k,m):

%o     if (k==1 or k==n): return 1

%o     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)

%o def A172018(n): return T(2*n-1, n, 3)/n

%o [A172018(n) for n in (1..30)] # _G. C. Greubel_, Mar 16 2022

%Y Cf. A142458, A172010.

%K nonn

%O 1,2

%A _Roger L. Bagula_, Nov 19 2010

%E Offset changed and more terms added by _G. C. Greubel_, Mar 16 2022